Men at Work has lost their final bid to prove they did not steal the distinctive flute riff of their 1980s hit Down Under from a children's campfire song.

The High Court on Friday denied the band's bid to appeal a Federal Court judge's earlier ruling that the group had copied the signature flute melody from the song Kookaburra Sits in the Old Gum Tree.

Kookaburra was written more than 70 years ago by Australian teacher Marion Sinclair for a Girl Guides competition.

Sinclair died in 1988, but publishing company Larrikin Music - which now holds the copyright for Kookaburra - filed a copyright lawsuit in 2009.

Last year, Federal Court Justice Peter Jacobson ruled that the Down Under flute riff replicated a substantial part of Sinclair's song.

The judge later ordered Men at Work's recording company, EMI Songs Australia, and Down Under songwriters Colin Hay and Ron Strykert to pay 5 per cent of royalties earned from the song since 2002 and from its future earnings.

The court did not specify what the penalty translates to in dollars.

Larrikin was not able to seek royalties earned before 2002 because of a statute of limitations.

Lawyers for Men at Work's recording companies maintained the band had not copied anything, and vowed to fight the ruling.

But Friday's decision from the High Court ends the band's chance to appeal.

Down Under and the album it was on, Business As Usual, reached number one on the Australian, American and British charts in early 1983.